The 21-year-old started six games and made 33 substitute appearances for Well but was loaned out to Queen of the South in the final few months of last season.
A Motherwell statement read: "With his contract due to expire at the end of the current campaign, the club has allowed the player to move to Rugby Park, but has protected its interests with a sizeable sell-on clause."
Meanwhile, Thomas's former boss Stephen Robinson is quoted by Sky Sports News as saying: "I wanted to have a look at Dom over the first few weeks of pre-season, but he expressed a desire to move on.
"This deal allows the lad to try and advance his career but also protects Motherwell's interests in the longer term, so it suits all parties."
Thomas originally moved to Motherwell from Celtic's youth set-up in 2014.